Work

Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems

Year: 2019

Type: article

Abstract: We study dynamical optimal transport metrics between density matrices associated to symmetric Dirichlet forms on finite-dimensional $$C^*$$ C ∗ -algebras. Our setting covers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, and spectral gap estimates.

Source: Journal of Statistical Physics

DOI: 10.1007/s10955-019-02434-w

Authors: Eric A. Carlen, Jan Maas

Institutions: Rutgers, The State University of New Jersey, Institute of Science and Technology Austria

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,690